A group of students wants to develop a calculator to reduce a fraction. The steps to do so are laid out in their math book as follows:%0D%0A%0D%0AExpress both the numerator (top number) and denominator (bottom number) as a product of their prime factors.%0D%0AStrike out any common factors.%0D%0AMultiply the remaining numbers to obtain the reduced numerator and denominator.%0D%0AWhich of the following elements would be appropriate to use in the algorithm?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Aa queue and a stack to pop out the prime factors for comparison%0D%0Aa queue and a stack to pop out the prime factors for comparison%0D%0A%0D%0Atwo stacks to pop out the prime factors for comparison%0D%0Atwo stacks to pop out the prime factors for comparison%0D%0A%0D%0Atwo lists to hold the prime factors for comparison%0D%0Atwo lists to hold the prime factors for comparison%0D%0A%0D%0Atwo queues to pop out the prime factors for comparison%0D%0Atwo queues to pop out the prime factors for comparison
Two lists to hold the prime factors for comparison would be appropriate to use in the algorithm.
The appropriate elements to use in the algorithm would be:
- Two stacks to pop out the prime factors for comparison.
To develop a calculator to reduce a fraction using the steps mentioned, the appropriate data structures to use in the algorithm are a queue and a stack to pop out the prime factors for comparison.
Here's why:
Step 1: Express the numerator and denominator as a product of their prime factors.
To accomplish this, you can start by dividing both the numerator and denominator by the smallest prime number, then continue dividing by the next prime number until the result is no longer divisible by any prime number. By using a stack, you can push the prime factors of the numerator and denominator onto the stack.
Step 2: Strike out any common factors.
To compare the prime factors of the numerator and denominator and strike out common factors, you can use a queue to pop out the prime factors for comparison. By comparing the prime factors one by one, you can remove the common factors from both the numerator and denominator.
Step 3: Multiply the remaining numbers to obtain the reduced numerator and denominator.
After removing the common factors, you will be left with the reduced numerator and denominator. To perform the final multiplication, you can use the stack to pop out the remaining prime factors from both the numerator and denominator and multiply them together.
Therefore, based on the steps provided in the math book, using a queue and a stack to pop out the prime factors for comparison would be the appropriate choice for the algorithm.